Measuring small angular deflections quickly, precisely, and accurately is an important capability that can be used in many areas. For example, such a capability is important in many fields of experimental physics. As a specific example, in the Eot-Wash experimental gravity group at the University of Washington, torsion balance experiments have been conducted that depend on the ability to measure minuscule angular deflections. (see, e.g., S. Schlamminger, K. Y. Choi, T. A. Wagner, J. H. Gundlach, and E. G. Adelberger, “Test of the equivalence principle using a rotating torsion balance,” Phys. Rev. Lett. 100, 041101 (2008); and G. L. Smith, C. D. Hoyle, J. H. Gundlach, E. G. Adelberger, B. R. Heckel, and H. E. Swanson, “Short-range tests of the equivalence principle,” Phys. Rev. D 61, 022001 (1999)).
The most commonly used device for measuring small angular deflections is an optical autocollimator. An optical autocollimator collimates the light of a point source using a collimating lens, reflects the collimated light off a target mirror, and then focuses the reflected light onto a position-sensitive photodetector using the collimating lens. Autocollimators are insensitive to displacements of the target, eliminate the effect of optical aberrations in the lens, and average over the reflecting surface of the target. Angular deflection measurements can also be made by a homodyne interferometer, which compares the path length of beams incident on two separate locations on the target.
While existing autocollimators can have a sensitivity of approximately 1 nrad/√{square root over (Hz)}, devices with even greater sensitivity that are insensitive to displacements of the target are desirable.